Welcome to the forum!
Unfortunately even a blood test won't be able to tell you anything about his breed - they only work if you are pretty certain of the parents but want confirmation, so you check that the DNA matches. There is no test for breeding (to my eternal frustration lol) because horses' breeds diversified relatively recently so there is no identifiable difference in their DNA such as there would be between a horse and another equid (for example).
What you could do is try and follow the ownership trail back to the original breeders as they'll know. This would be considerably more difficult with an older horse or one bred by a "backyard" breeder rather than a professional stud but if you get up some pictures of him and give us as much info as you have then you may be lucky enough to find someone who knew him previously and has more info on his past. Otherwise, some knowledgeable forum members can give you an (educated) guess as to his breed.